See Inside

# Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups" [Preview]

A new set of puzzles inspired by Rubik's Cube offers puzzle lovers the chance to get acquainted with the secret twists and turns of mathematical entities called sporadic simple groups

ANIMATED NUMBERS perform an imagined dance as they rearrange themselves according to the "merge" move in the authors' new "M12" puzzle—one of three "sporadic simple" puzzles the two have created. Image: Matt Collins

### In Brief

• Success in “solving” Rubik’s Cube depends on discovering short se­quences of moves that accomplish limited goals.
• But the strategy is so successful that the authors yearned for puzzles whose solutions would require novel tactics.
• Basing their work on the mathematical theory of groups so well illustrated by Rubik’s Cube, the authors have devised three new games that challenge today’s generation of puzzle lovers with the complexities of “sporadic simple groups.”

• Sidebar

• Sidebar

• Sidebar

#### Puzzles: Simple Groups at Play

Editor's Note: The online puzzles mentioned in the July magazine can be found here.

Millions of people have been perplexed at one time or another by Rubik’s Cube, a fascinating puzzle that took the world by storm in the 1980s. If you somehow missed the puzzle—or the 1980s—the cube is a plastic gizmo that appears to be made up of 27 small cubes, or “cubies,” stacked into a larger cube, three cubies to an edge. Each of the six square faces of the larger cube is colored in one of six eye-catching colors—typically blue, green, orange, red, yellow or white. We said the cube appears to be a stack of cubies, but appearances here are deceptive. An ingenious mechanism, invented in 1974 by a Hungarian teacher named Erno Rubik (and, independently, in 1976 by a Japanese engineer named Terutoshi Ishige), enables any of the six square faces of the large cube to be twisted about the center of that face. Twist the faces in some random sequence five or six times, and you have a cube so scrambled that only an expert—a cubemeister—can restore order. The object of the puzzle is to put an arbitrarily scrambled cube back into its original state, one solid color per face, thereby “solving” the cube.

Already a Digital subscriber? Sign-in Now

View
1. 1. gaffy16 04:16 AM 7/11/08

i want to know how to play rubik's cube.......

2. 2. wwarren777 01:35 PM 7/18/08

I do not see where we can download the games, as I think was mentioned in the article.

3. 3. wilsomer in reply to wwarren777 11:13 PM 7/19/08

Need group game.

4. 4. Pilcrow 04:53 AM 7/21/08

OK, I bought the magazine, read the article. It said there were 3 puzzles available. WHERE ARE THEY?

5. 5. Pilcrow 04:57 AM 7/21/08

phooey

6. 6. amoulder 06:24 AM 7/21/08

I I also tried to get the three puzzles and was unable to find them.
The article is as always very interesting. I am just disappointed to be unable to get the extra texts.

7. 7. amoulder 05:51 AM 7/22/08

Has it got a special file all of its own and my computer doesn't recognise it ?

8. 8. mistygris 07:15 PM 7/22/08

how do I download the puzzles? The article says the 3 games are available online?

9. 9. wimknoop in reply to mistygris 01:19 PM 7/25/08

10. 10. Moose 12:35 PM 8/18/08

http://www.sciam.com/article.cfm?id=puzzles-simple-groups-at-play

11. 11. sakanamikan in reply to Pilcrow 10:59 PM 8/24/08

http://www.sciam.com/media/inline/2008-07/puzzles/m12.html
http://www.sciam.com/media/inline/2008-07/puzzles/m24.html
http://www.sciam.com/media/inline/2008-07/puzzles/dotto.zip

12. 12. sakanamikan in reply to Pilcrow 11:01 PM 8/24/08

http://www.sciam.com/media/inline/2008-07/puzzles/m12.html
http://www.sciam.com/media/inline/2008-07/puzzles/m24.html
http://www.sciam.com/media/inline/2008-07/puzzles/dotto.zip

13. 13. 91supernova91 05:40 AM 9/23/08

blablabla im on school --_-- but damn these puzzle im doing it on school now and one next to me solves a 5x5 in 47 seconds damn hes good whatever we try to hussle he will pass in 50 sec at max.

14. 14. 91supernova91 05:42 AM 9/23/08

blablabla im on school --_-- but damn these puzzle im doing it on school now and one next to me solves a 5x5 in 20 sec with one hand without even looking really at it he just looks how weve put it and wham,,,,, damn hes good whatever we try to hussle he will pass in 20 sec at max. he just looks ho we had put it puts it in one hand and begins to hussle just to fast we cant follow it :P

15. 15. 91supernova91 in reply to 91supernova91 05:42 AM 9/23/08

...

16. 16. 91supernova91 05:43 AM 9/23/08

good lord his mate is even better, hes the real god in it XD

17. 17. 91supernova91 05:43 AM 9/23/08

good lord his mate is even better,

18. 18. ebuck 06:44 PM 3/31/09

the magazine that I PAY to subscribe to SciAm says the puzzles are here; now that I get here you want to PAY again!!! NO WAY!! And further I will not renew. Your absolute GREED is appalling

19. 19. gogsy 01:31 PM 5/29/09

very impressive

20. 20. gogsy 01:32 PM 5/29/09

very impressive

21. 21. speedfreak 10:25 AM 12/28/09

i know how to solve robic's cube but in another way than the one in the article
and I find my way alot easier and faster
and if any one found the puzzles please tell me where they are

You must sign in or register as a ScientificAmerican.com member to submit a comment.
Click one of the buttons below to register using an existing Social Account.

## More from Scientific American

• Scientific American Magazine | 2 hours ago

### Teenage Flu Scientist Shares His Recipe for Prizewinning Research

• Scientific American Magazine | 2 hours ago

• @ScientificAmerican | 17 hours ago

### Can We Harness Disruption to Improve Our World's Future?

• News | 18 hours ago

### Federal Flood Maps Left New York Unprepared for Sandy, and FEMA Knew It

• News | 20 hours ago

More »

## Latest from SA Blog Network

• ### Physics Week in Review: December 7, 2013

Cocktail Party Physics | 5 hours ago
• ### Wonderful Things: The Pugnacious, Alien-esque Skeleton Shrimp

The Artful Amoeba | 15 hours ago
• ### Can We Harness Disruption to Improve Our World's Future?

STAFF
@ScientificAmerican | 17 hours ago
• ### British Storm Brings Up History's First Work of Social Media

Plugged In | 18 hours ago
• ### Rolling on Wheels That Aren t Round

Observations | 18 hours ago

## Science Jobs of the Week

Rubik's Cube Inspired Puzzles Demonstrate Math's "Simple Groups": Scientific American Magazine

X

Give a 1 year subscription as low as \$9.99

X

X

###### Welcome, . Do you have an existing ScientificAmerican.com account?

No, I would like to create a new account with my profile information.

X

Are you sure?

X